A density bound for efficient packings of 3-space with centrally symmetricconvex bodies

It is shown that every compact convex set K which is centrally symmetric an d has a non-empty interior admits a packing of Euclidean 3-space with densi ty at least 0.46421.... The best such bound previously known is 0.30051...d ue to the theorem of Minkowski-Hlawka. It is probable that there is such a lower bound which is significantly greater than the one shown in this note, since there is a packing of congruent spheres which has density pi/root 18 = 0.74048....